We see so little of the Comic Strip ensemble these days that it's easy to forget how long they've been in the trenches of British spoof, tossing out a grenade every now and then, as if cursed to spend the rest of their days striving to match the perfection of their hilarious first episode, Five Go Mad in Dorset, which introduced high jinks to Channel 4's inaugural broadcast in 1982 and the term "lashings of ginger beer" to the cultural memory.

The Hunt for Tony Blair – a parodic splicing of noughties politics and 1950s British film noir (though what Herman's Hermits were doing on the soundtrack I don't know) – wasn't uproariously funny but it was handsomely made, with melodramatic shadows and enough money for fog, flat-footed policemen and steam trains. The plot, such as it was – a madcap chase across country, with the PM on the run for murder – threw up knockabout humour and vignettes from Blair's WMD fiasco, featuring a cast of the usual suspects: a languid Nigel Planer as Mandelson; Harry Enfield in East End shout mode as "Alastair"; the excellent Jennifer Saunders as Thatcher in her dotage (and full Barbara Cartland drag), watching footage of her Falklands triumphs from a chaise longue.

Director Peter Richardson, whose comic talents aren't seen enough on screen, played George Bush as a rasping B-movie Italian mobster ("I'm gonna get straight to the crotch of the matter here"). With the exception of impressionist Ronni Ancona (whose 10 seconds as Barbara Windsor seemed puzzlingly extraneous), no one went for a direct impersonation. Stephen Mangan didn't make a bad Blair, though he could have worked on the grin, and he couldn't quite make his mind up between feckless and reckless as he capered from one mishap to the next leaving a trail of bodies. Did Blair's moral insouciance ("Yet another unavoidable death, but, hey, shit happens") call for a look of idiocy or slipperiness?

The comedy had mischief at its heart in mooting that Blair had bumped off his predecessor, John Smith, and accidentally pushed Robin Cook off a Scottish mountain, while Robbie Coltrane's Inspector Hutton (aha!) tacitly invoked the spectre of Dr David Kelly (we never found out who Blair was charged with murdering). But it was hard to squeeze fresh satire from the overfamiliar stodge of the politics ("Tell Gordon to run the country and trust the bankers"). Mangan was at his funniest hiding among sheep in the back of a truck or kicking Ross Noble (playing an old socialist) off a speeding train, though there was amusement elsewhere. I had to laugh at variety theatre act Professor Predictor, shoehorned into the story to enable Rik Mayall in a bald wig and boffin glasses to answer questions from the audience. Would the Beatles still be at No 1 in 50 years' time?

"No. The Beatles will no longer exist. But Paul McCartney will marry a woman with one leg."

How the audience roared. "Pull the other one," someone shouted. Arf, arf.

My heart sank a little when Joanna Lumley started her Greek Odyssey with the words: "I'm in Athens, the capital of Greece." Well, OK, I suppose she could have meant the one in Ohio. But it wasn't long before she won me over, not least by climbing what looked like a homemade ladder to the top of the Acropolis to watch restorers scraping away, using toothbrushes and dentists' drills. You wouldn't have got me up there. "Don't look down," said her interpreter. Joanna, bless her, tried to take her mind off her vertigo by telling us about the traumatic day she got stuck on a ladder as a girl and had to be rescued. She was only up here now, she said, out of duty to the viewers. "Because I love you," she said, shooting a toothy smile at the camera.

After a day at the ruins she was ready for a night on the town and was soon heading for a club where it was tradition for the customers to pay 60 euros for a plate of flowers to throw at a singer on stage. Apparently, a wild evening here could cost five grand. Economic crisis? Pah!

"We live only for this day," reasoned one reveller. "Tomorrow, maybe everything boom!" Maybe? Still, it was good to see philosophy alive and kicking in the home of Aristotle and Plato.

There were gods to be worshipped, in particular 1960s bespectacled diva Nana Mouskouri, whom Joanna met at the remains of a huge amphitheatre. She was taken aback when Joanna asked her to sing, but she didn't need asking twice. The tourists were stilled as Nana trilled, as if required to observe a minute's silence. Joanna does make friends easily. She wooed the odd women of Evia who communicated by whistling at each other. They could speak, too, but if you wanted to banter with a goat on a roof – as one did – only whistling would do. Admittedly, the goats could only say "meh" but frankly it's eerie to see one converse in any tongue. Whistling was a dying language, though, with most of the children in the tiny community of 40 unwilling to learn it, perhaps seeing English or Chinese as a more attractive option in an increasingly competitive global marketplace.

Then on a remote peninsula, Joanna stumbled upon an old woman living in a deserted hill village. Everyone had left, she said, when they built a road in the 70s. What on earth did she live on? For her answer she took Joanna out to forage for wild asparagus, which she cooked with oil and salt, and lemons as "sweet as oranges". Tucking in, Joanna asked if she didn't get lonely out here in this ghost town in the middle of nowhere. "I'm not afraid of anything," she said. Homer would have put her on the itinerary.

Art's tough girl Tracey Emin has spent her career answering the question Who Do You Think You Are?, or at least creating an effigy of who she wants us to think she is. As a medium of revelation itself, WDYTYA? admits no such cunning. After all, you can't choose your own family. Tracey was a nervous wreck. Would she get the ancestors she deserved – gritty swashbucklers, salts of the earth, creative mavericks – or would they turn out to be loss adjusters from the home counties?

It didn't start well, with maternal great-grandfather Henry having been a product of reform school. Tracey's inventive mind fizzed with wishful thinking. Perhaps young Henry had been plucked out of poverty and earmarked for an education by a rich patron, impressed by his native gifts and promise? In fact, he had stolen two brass taps. But, hang on, he had a spotless record during his years there and acquired skills with saw and lathe that would stand him in good stead if he now emigrated to Canada, which was all the rage with former inmates. Tracey's eyes lit up, but no – he burgled a house instead and stole some cocoa, £8 and a violin. Tracey was sad for poor Henry (whose mother had died) but not without hope: "Maybe he wanted the violin to play," she suggested, adding that there had been guitar players in the family.

Perhaps, said the researcher gently. Tracey blamed the father, but then it transpired that he'd done a year's hard labour for thieving in the 1880s, when hard labour meant walking the treadwheel six hours a day – and that was the equivalent of climbing Ben Nevis twice, said the narrator, who throughout this fascinating programme talked us through pictures of grimy urchins, old lags and scenes of corrective punishment.

But just as Tracey was losing heart, the next archive provided thrilling evidence of a "besom-maker" in the family and then, blimey, a line of tent-dwellers, pedlars, tinkers and Gypsies as long as your arm – kindred free spirits to the blood and bone! Tracey's face said it all. You couldn't make it up and yet it looked as if someone just had.